Police have begun their search of the home of a couple shot dead with two other victims on a secluded French hillside.

A team of four French officers has travelled to Britain to work with UK detectives at the house of Saad al-Hilli in Claygate, Surrey.

Iraqi-born Hilli, 50, was shot in his car along with his wife, Iqbal, in the French village of Chevaline on Wednesday. The couple and a 77-year-old Swedish woman and a French cyclist were killed by a bullet to each of their heads.

The couple's four-year-old daughter Zeena lay undiscovered under her mother's body for eight hours after the murders. Her sister, Zainab, eight, who was shot in the shoulder and suffered severe head injuries after being beaten, remains in a medically induced coma in hospital in Grenoble. Doctors report her condition as stable and improving.

Two relatives of the Hilli family and a British social worker have travelled to France and will visit the girls, who are under police supervision, according to reports.

However it was unclear when they would be able to see Zainab as she continues to be treated in hospital.

French investigators are expected to reveal the results of postmortem examinations of the four killed.

Officers from Surrey police erected a tent at the front of the Hillis' house on Saturday as they prepared to search the property with the French police team, led by Marc de Tarle.

In a joint statement by British and French officers outside Woking police station, Assistant Chief Constable Rob Price said: "This is a French-led investigation."

The French prosecutor Eric Maillaud said investigators were told of a possible feud between Hilli and his brother over money, but the sibling had gone to a police station to deny the row.

Maillaud said he had not heard about any possible inheritance issue and that Zaid remained "a free man".

Zeena has spoken to police and confirmed that two of the victims were her parents, but said she did not know the Swedish woman very well, although she has been identified as her grandmother in some reports.

The other man killed was Sylvain Mollier, 45, a French cyclist from the area, who appears to have been passing the scene when he got caught up in the attack.

Maillaud said Zeena remained under the care of psychiatric teams and had spoken about what he described as the "terror" of what happened, but did not see anything because she was hiding.

"The witness statement of the four-year-old girl, she just talked about a fury, a terror. She explained that from the beginning of the murder she was already between her mother and that other woman and she rushed under her mother's legs, her mother's skirt," Maillaud said.

"I imagine she'll go back to Britain in a short timescale. We have to be able to identify members of her family, we have to make sure that they are people that can be trusted. You can imagine that we cannot entrust that little girl to the first person that turns up."

Her sister was not yet well enough to be interviewed but it was hoped she could provide vital details of the attacker or attackers.

Witnesses have said they saw a green four-wheel-drive vehicle in the area at the time of the killings, and possibly a motorbike.

The Surrey police force said it was assisting the French authorities as they carried out a "complex" investigation.

"As part of this, the force is facilitating a visit by French investigators to conduct inquiries in the UK," a spokesman said.

Italian and Swiss police are helping with the investigation because of the proximity of the attack to their borders. The Hilli family is also understood to own property in Switzerland.